Question Number 28288 by Mr eaay last updated on 23/Jan/18
![](https://www.tinkutara.com/question/3287.png)
Answered by Rasheed.Sindhi last updated on 23/Jan/18
![^• (2+(√3) )^(−1) =(1/(2+(√3)))×((2−(√3))/(2−(√3))) =2−(√3) ^• (2+(√3))^2 =(2)^2 +2(2)((√3))+((√3) )^2 =7+4(√x) ^• (2+(√3))^3 =(2)^3 +((√3))^3 +3(2)^2 ((√3) )+ 3(2)((√3) )^2 =8+3(√3) +12(√3) +18 =26+15(√3) The given equation⇒ ( (2+(√3))^3 )^x −5((2+(√3))^2 )^x +6(2+(√3))^x +((2+(√3))^(−1) )^x =5 ( (2+(√3))^x )^3 −5((2+(√3))^x )^2 +6(2+(√3))^x +((2+(√3))^x )^(−1) =5 Let (2+(√3) )^x =y ⇒ y^3 −5y^2 +6y+y^(−1) =5 y^4 −5y^3 +6y^2 −5y+1=0 ⋮](https://www.tinkutara.com/question/Q28292.png)
Commented by Rasheed.Sindhi last updated on 23/Jan/18
��şίŕ ţħάήķş ғόŕ ςόŕŕέςţίόή!��
Answered by ajfour last updated on 23/Jan/18
![x=±1](https://www.tinkutara.com/question/Q28307.png)